When attempting to build a custom web application from either a web map or from scratch, the Download button for default app templates does not appear in the Create a New Web App dialog window.
This issue occurs due to the ArcGIS Online Organization account referencing a custom configurable apps group. The Esri Default Templates may not be shared to this group and this causes problems when trying to download or create apps from these templates.
To resolve this issue, do the following:
Note: Ensure the 'Share the Esri default configurable apps to this group when you click Save.' option is checked.
In the event the default templates still do not appear when creating the custom app, as an alternative, re-create the group and reconfigure the custom group settings.